Respuesta :
Answer:
a)
i) p(x) = 1.4 s(x)
ii) s(x) = p(x) ÷ 1.4 = [p(x)]/1.4
b)
i) p(x) = [s(x) + 200]
ii) s(x) = [p(x) - 200]
c)
i) p(x) = s(x+4)
ii) s(x) = p(x-4)
Step-by-step explanation:
Complete Question
Each summer Primo Pizza and Pizza Supreme compete to see who has the larger summer profit. Let p(x) represent Primo Pizza's profit (in dollars) x days after June 1. Let s(x) represent Pizza Supreme's profit (in dollars) x days after June 1.
a) Suppose Primo Pizza's profit each day is 1.4 times as large as the profit of Pizza Supreme
i. Write a function formula for p using the function s.
ii. Write a function formula for s using the function p.
b) Suppose Primo Pizza's profit each day is $200 more than the profit of Pizza Supreme.
i) Write a function formula for p using the function s.
ii) Write a function formula for s using the function p.
c) Suppose Primo Pizza's profit on a given day is always the same as the profit of Pizza Supreme's profit 4 days later.
i) Write a function formula for p using the function s.
ii) Write a function formula for s using the function p.
The profits per day for Primo Pizza, x days after June 1 = p(x)
The profits per day for Supreme Pizza, x days after June 1 = s(x)
a) Primo Pizza's profits per day is 1.4 times that of Supreme Pizza's per day.
Primo Pizza's profits per day, x days after June 1 = p(x)
Supreme Pizza's profit per day, x days after June 1 = s(x)
i) p(x) = 1.4 s(x)
ii) s(x) = p(x) ÷ 1.4 = [p(x)]/1.4
b) Primo Pizza profits per day is $200 more than that of Supreme Pizza
Primo Pizza's profits per day, x days after June 1 = p(x)
Supreme Pizza's profit per day, x days after June 1 = s(x)
i) p(x) = [s(x) + 200]
ii) s(x) = [p(x) - 200]
c) Primo Pizza's profit on a given day is always the same as the profit of Pizza Supreme's profit 4 days later.
Primo Pizza's profits per day, x days after June 1 = p(x)
Supreme Pizza's profit per day, x days after June 1 = s(x)
Supreme Pizza's profit per day, 4 days later = s(x+4)
So,
i) p(x) = s(x+4)
ii) This means that Supreme Pizza's profit per day is the same as Primo Pizza's profit per day four days ago.
Primo Pizza's profit per day four days ago = p(x-4)
So,
s(x) = p(x-4)
Hope this Helps!!!
(i) The required formula [tex]p[/tex] is [tex](p(x))=(s(x+3))[/tex]
(ii)The required formula [tex]s[/tex] is [tex](s(x))=(p(x-3))[/tex]
Function:
A function is defined as a relation between a set of inputs having one output each.
Given that,
[tex]p(x)[/tex] represents the prime's pizza's profit and [tex]s(x)[/tex] represents the supreme's pizza's profit.
(i): The required function formula is,
[tex](p(x))=(s(x+3))[/tex]...(1)
Since [tex]x[/tex] represents the number of days.
(ii): Now, replace [tex]x\ by\ (x-3)[/tex] into the equation (1) we get,
[tex](p(x-3))=(s(x-3+3))\\(p(x-3))=(s(x))\\(s(x))=(p(x-3))[/tex]
Learn more about the topic Function:
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